Onsager, Lars (1903–1976)

Lars Onsager was a Norwegian-American chemist and physicist who received the 1968 Nobel Prize in Chemistry for "the discovery of the reciprocal relations bearing his name which are fundamental for the thermodynamics of irreversible processes."

Onsager was born on November 27, 1903, to Ingrid and Erling Onsager. The family lived in Oslo (then Kristiania), Norway, where his father was a barrister. He grew up with two younger brothers, Per and Knut. Onsager's mathematical acumen was apparent early. At the age of fifteen he discovered for himself how to solve cubic equations. His school performance enabled him to skip one year at school, and at the age of sixteen he was ready for university studies. He entered the Norwegian Institute of Technology at Trondheim, where he graduated in 1925 with a chemical engineering degree.

As a freshman in Trondheim, he had studied the most recent theory, attributed to Peter Debye and Erich Hückel, of electrolytic solutions, a topic to which he returned continually throughout his life. His first contact with the scientific world was when he, at the age of twenty-two, entered Debye's office in Zürich, saying without introducing himself: "Good morning, Herr Professor, your theory of electrolytic conduction is incorrect" (Hemmer et al., 1996). Debye, impressed by Onsager's arguments, hired him as his assistant. Onsager's revision of the Debye-Hückel theory resulted in the so-called Onsager limiting law for electrolytic conduction, an important result in good agreement with experiments.

In 1928 Onsager emigrated to the United States, first to Johns Hopkins University, then in the same year to Brown University. Here he struggled with an attempt to base symmetry relations found in his work on electrolytes on general physical laws. Thus he considered more general irreversible processes than conduction and diffusion, the basic ingredients in electrolytic conduction. Irreversible transport processes are centered around fluxes of matter, energy, and electric charge and their dependence upon the forces that give rise to them. The processes are called irreversible because the fluxes are unidirectional and cannot run in the reverse direction. The main effects are well-known: diffusion (transport of matter) due to a concentration gradient or concentration difference (e.g., across a membrane), heat conduction (transport of energy) due to a temperature gradient or temperature difference, and electrical conduction (transport of electric charge) due to a potential difference.

However, a potential may give rise to more than one type of flux. There are cross-effects: A temperature difference can also result in diffusion, called thermal diffusion, and a concentration difference can result in a heat current. The general relation between fluxes J_i and the driving potentials X_i is of the form of linear relations with coefficients L_ij, when the fluxes are not too great. Onsager showed that the coefficients of the cross-effects were equal: These are the famous Onsager reciprocal relations. Thus there is symmetry in the ability of a potential X_i to create a flux J_j, and of the ability of a potential X_j to create a flux J_i. The reciprocal relations are experimentally verifiable connections between effects which superficially might appear to be independent.

Such symmetries had been noticed in special cases already in the nineteenth century. One example was heat conduction in a crystal, where the X_i are the temperature gradients in the three spatial directions. Cross-effects between electric conduction and diffusion, and between heat conduction and diffusion, were also studied. Reciprocal relations of the form L_ij = L_ji were confirmed experimentally for these cases, but a general principle, from which these would follow, was lacking. This situation changed dramatically in 1931 when Onsager, then at Brown University, derived the reciprocal relations. In the derivation, Onsager used the fact that the microscopic dynamics is symmetric in time, and he assumed that microscopic fluctuations on the average follow macroscopic laws when they relax towards equilibrium. The Onsager formulation was so elegant and so general that it has been referred to as the Fourth Law of Thermodynamics. It is surprising to note that the immediate impact of Onsager's work, which later earned him the Nobel Prize, was very minor, and that it was virtually ignored during the following decade.

Onsager spent the summer of 1933 in Europe. During a visit to the physical chemist Hans Falkenhagen, he met Falkenhagen's sister-in-law, Margrethe (Gretl) Arledter. They fell in love and married in September the same year. Another important event in 1933 was Onsager's move to Yale University, where he remained until his retirement. In the course of time the Onsager family grew to include one daughter and three sons. At Yale he was first a Stirling and Gibbs fellow, then assistant professor, associate professor, and finally in 1945 J. Willard Gibbs Professor of Theoretical Chemistry.

Although Onsager's first appointment at Yale was a postdoctoral fellowship, he had no doctorate. It disturbed him that everybody called him "Dr. Onsager," and he decided to seek the Ph.D. from Yale. He was told that any of his published works would do for the thesis, but he felt he should write something new, and he quickly submitted a lengthy dissertation on Mathieu functions. Both the Department of Chemistry and the Department of Physics, found it difficult. The Department of Mathematics, however, was enthusiastic and was prepared to award the degree, whereupon the Department of Chemistry did not hesitate in accepting the thesis.

If Onsager's great achievement with the thermodynamics of irreversible processes met with initial indifference, Onsager's next feat created a sensation in the scientific world. In a discussion remark in 1942, he disclosed that he had solved exactly the two-dimensional Ising model, a model of a ferromagnet, and showed that it had a phase transition with a specific heat that rose to infinity at the transition point. The full paper appeared in 1944. For the first time the exact statistical mechanics of a realistic model of an interacting system became available. His solution was a tour de force, using mathematics almost unheard of in the theoretical physics of the day, and it initiated the modern developments in the theory of critical phenomena. Basing their decision especially on this work, the faculty at Cornell University nominated Onsager for the Nobel Prize in both physics and chemistry.

Although the reciprocal relations, electrolyte theory, and the solution of the Ising model were high-points in Onsager's career, he had broader interests. From about 1940 Onsager became active in low-temperature physics. He suggested the existence of quantized vortices in superfluid helium, and provided the microscopic interpretation of the oscillatory diamagnetism in metals. In 1949, four years after he became an American citizen, he laid the foundation for a theory of liquid crystals. In his later years he studied the electrical properties of ice and took much interest in biophysics.

The importance of Onsager's work on irreversible processes was not recognized until the end of World War II, more than a decade after its publication. From then on irreversible thermodynamics gained momentum steadily, and the reciprocal relations have been applied to many transport processes in physics, chemistry, technology, and biology. The law of reciprocal relations was eventually recognized as an enormous advance in theoretical chemistry, earning Onsager the Nobel Prize in 1968. Thus more than a third of a century passed before Onsager's work was suitably recognized. In his presentation speech at the Nobel ceremonies S. Claesson said: "Here we thus have a case to which a special rule of the Nobel Foundation is of more than usual applicability. It reads: 'Work done in the past may be selected for the award only on the supposition that its significance has until recently not been fully appreciated.'"

Onsager was reluctant to publish. Many of his original discoveries appeared first in the discussion periods at scientific meetings and were not published for years, if at all. He was very much an individualist. Although he had students and coworkers, especially in his later years, he preferred to work alone. Therefore, he never created a school around him. As a person, Onsager was modest and self-effacing, with a wry sense of humor. He had an awesome memory and was at ease with history, language, and the literature of the West. Games of all kinds appealed to him.

After retirement he went to the Centre for Theoretical Studies at Coral Gables, Florida, where one of his main interests was the question of the origin of life. He died at Coral Gables on October 5, 1976.

Thermodynamics.

Hemmer, P.C., Holden, H., and Ratkje, S. Kjelstrup, eds. (1996) The Collected Works of Lars Onsager. Singapore: World Scientific.

Onsager, L. (1931) "Reciprocal Relations in Irreversible Processes." Physical Review 37:405–426 and 38:2265–2279.

This is the complete article, containing 1,459 words (approx. 5 pages at 300 words per page).